Method and a demodulator for demodulating a position error signal from a readback servo signal

ABSTRACT

According to embodiments of the present invention, a method for demodulating a position error signal from a readback servo signal having a first frequency associated with a first servo track of a storage medium and a second frequency associated with a second servo track adjacent to the first servo track is provided. The method includes sampling the readback servo signal at successive time instants to provide a sequence of samples, computing a Discrete Fourier Transform based on the sequence of samples, and providing a measurement indicative of the position error signal based on the Discrete Fourier Transform. According to further embodiments of the present invention, a demodulator is also provided.

CROSS-REFERENCE TO RELATED APPLICATION

This application claims the benefit of priority of Singapore patentapplication No. 201108624-6, filed 21 Nov. 2011, the content of it beinghereby incorporated by reference in its entirety for all purposes.

TECHNICAL FIELD

Various embodiments relate to a demodulator and a method fordemodulating a position error signal.

BACKGROUND

Electronic devices, including mobile computing and/or communicationdevices, are becoming smaller thereby driving the weight and size ofdata storage devices down, while requiring large storage capacity in theterabyte range and low power consumption. An increasing storage capacitywould require the need for increased precision in tracking the movementof the read/write head.

Data storage devices, such as hard disk drives (HDDs), employ servosystems for tracking and controlling the movement of the read/writehead. Conventional servo systems employ embedded servo where the servoinformation runs radially from the inner diameter (ID) to the outerdiameter (OD) of the disc in a series of “servo wedges” interspersedwith data. Therefore, the servo information is only detected when theread/write head moves over these servo wedges. In between the servowedges, no servo information is received by the head. Conventional servosystems typically employ ABCD servo-burst-signal pattern, from which theposition error signal (PES) is determined. In systems employing the ABCDservo-burst-signal pattern, position information is derived, forexample, from the relative amplitudes of the A burst to the B burst.Furthermore, conventional servo systems also employ frequency servoschemes for PES demodulation, where the position information is derivedfrom the relative amplitudes of one frequency to another frequency of aservo signal.

FIG. 1A shows a general schematic block diagram for a conventional servocontrol system 100. The servo controller 106 is the heart of the system100 that provides a control signal to the plant 110. Plant input noised_(i) is injected at summer 108 and could include electronics noise inthe circuits of the system 100. The plant 110, in a hard disk drive(HDD), embodies the VCM (voice coil motor) and arm which control theposition of the head (e.g. read/write head). Plant output noise d_(o) isinjected into the system 100 at summer 112 before the signal y iscompared to the reference signal, ref., at summer 102, and includesvibrations in the system due to windage, NRRO (non-repeatable run-out)and external shock and vibe. The reference signal compared at summer 102represents the signal the controller 106 is attempting to follow andcould be an offset of the head due to a drift or disturbance. The signalpes_(t) is the true position error signal representing the actualdifference between the track center, and the head position. The true PESsignal, pes_(t), is contaminated or affected with additional noise n atsummer 104 before it is fed as input into the controller 106, closingthe servo control loop. The source of noise n at summer 104 could be dueto all the usual sources of noise in a recording system such aselectronics noise, thermal noise, or media noise. On adding this noiseto pes_(t), the pes signal that drives the controller 106 is obtained.

SUMMARY

According to an embodiment, a method for demodulating a position errorsignal from a readback servo signal having a first frequency associatedwith a first servo track of a storage medium and a second frequencyassociated with a second servo track adjacent to the first servo trackis provided. The method may include sampling the readback servo signalat successive time instants to provide a sequence of samples, computinga Discrete Fourier Transform based on the sequence of samples, andproviding a measurement indicative of the position error signal based onthe Discrete Fourier Transform.

According to an embodiment, a demodulator for demodulating a positionerror signal from a readback servo signal having a first frequencyassociated with a first servo track of a storage medium and a secondfrequency associated with a second servo track adjacent to the firstservo track is provided. The demodulator may include a sampling circuitconfigured to sample the readback servo signal at successive timeinstants to provide a sequence of samples, and a computing circuitconfigured to compute a Discrete Fourier Transform based on the sequenceof samples, and further configured to provide a measurement indicativeof the position error signal based on the Discrete Fourier Transform.

BRIEF DESCRIPTION OF THE DRAWINGS

In the drawings, like reference characters generally refer to like partsthroughout the different views. The drawings are not necessarily toscale, emphasis instead generally being placed upon illustrating theprinciples of the invention. In the following description, variousembodiments of the invention are described with reference to thefollowing drawings, in which:

FIG. 1A shows a general schematic block diagram of a conventional servocontrol system.

FIG. 1B shows a schematic block diagram of a servo control system,according to various embodiments.

FIG. 2A shows a schematic top view of a portion of a servo layer,according to various embodiments.

FIG. 2B shows a schematic top view of a section of the servo layer ofthe embodiment of FIG. 2A.

FIG. 3A shows a flow chart illustrating a method for demodulating aposition error signal from a readback servo signal, according to variousembodiments.

FIG. 3B shows a schematic block diagram of a demodulator fordemodulating a position error signal from a readback servo signal,according to various embodiments.

FIG. 4 shows an illustration of a sliding window tap-delay line,according to various embodiments.

FIG. 5 shows a plot of comparison of results of the sliding windowDiscrete Fourier Transform (DFT) of various embodiments and a directcomputational approach for extracting position error signal (PES).

FIG. 6A shows a plot of results corresponding to a demodulated positionerror signal (PES) with no servo control and no data layer noise,according to various embodiments.

FIG. 6B shows a plot of results corresponding to a demodulated positionerror signal (PES) with no servo control and with data layer noise,according to various embodiments.

FIG. 6C shows a plot of results corresponding to a demodulated positionerror signal (PES) with servo control and with no data layer noise,according to various embodiments.

FIG. 6D shows a plot of results corresponding to a demodulated positionerror signal (PES) with servo control and with data layer noise,according to various embodiments.

FIG. 7 shows some examples of servo patterns of a servo layer, accordingto various embodiments.

DETAILED DESCRIPTION

The following detailed description refers to the accompanying drawingsthat show, by way of illustration, specific details and embodiments inwhich the invention may be practiced. These embodiments are described insufficient detail to enable those skilled in the art to practice theinvention. Other embodiments may be utilized and structural, logical,and electrical changes may be made without departing from the scope ofthe invention. The various embodiments are not necessarily mutuallyexclusive, as some embodiments can be combined with one or more otherembodiments to form new embodiments.

Embodiments described in the context of a method are analogously validfor a device, and vice versa.

In the context of various embodiments, the articles “a”, “an” and “the”as used with regard to a feature or element includes a reference to oneor more of the features or elements.

As used herein, the term “and/or” includes any and all combinations ofone or more of the associated listed items.

Various embodiments relate to a data storage device or system having adedicated servo layer employing a dual frequency servo scheme. The servolayer may include servo information. Various embodiments employfrequency servo schemes for position error signal (PES) demodulation,where the position information may be derived from the relativeamplitudes of one frequency of a servo signal to another frequency ofthe servo signal. In the context of various embodiments, the servo layermay be arranged on a same side as a data recording layer on a disk, e.g.a platter, such that information from the servo layer and the data layermay be read and/or processed together.

Various embodiments relate to a demodulator and a method fordemodulating a position error signal in the frequency domain, forexample based on Discrete Fourier Transform (DFT), for example using anapproach employing a windowed DFT, e.g. a sliding windowed DFT.

In one implementation of the DFT, FFT algorithm may be employed forimplementing the DFT quickly, where the FFT may offer the fastest way toimplement the DFT for general inputs. In embodiments where the input hasa specific format, for example where the input to the DFT comes from atap-delay line, e.g. as shown in FIG. 4 and to be described later, in anon-limiting example, the DFT of a sliding window of the samplesx_(n-w+1) to x_(n) may be continuously updated using the formulations tobe described later. Without the condition of a tap-delay line, the FFTalgorithm may offer a suitable approach. With the pre-condition of atap-delay line input (e.g. a sliding window), then the updates of theDFT may be faster, being O(N), as compared to O(N log N) for the FFTalgorithm, where N is the window length and “O” is the big O notation asgenerally used in Mathematics to describe the limiting behavior of afunction when the argument/input of the function tends towards aparticular value or infinity. Therefore, the sliding window updateapproach may be employed, rather than the FFT algorithm, based on thetap-delay line input. In addition, the embodiment based on the DFTupdate has the benefit that where only a particular frequency bin(subscript k of X_(k)) is required, it may not be necessary to computethe DFT at all the other frequencies. In contrast, with the FFT, allfrequency bins need to be computed, and not just a practicular frequencybin (e.g. frequency bin 12 only).

In other words, the FFT is a complex algorithm for calculating the DFTin a general situation, while the sliding window DFT may be employed tocalculate the DFT in the embodiment when the input to the DFT comes froma tap-delay line (or sliding window). FFT is more general and is O(Nlog(N)), while sliding window DFT may be implemented when the inputcomes from a tap delay line and is O(N).

Various embodiments further relate to an efficient dual frequencyposition error signal (PES) demodulator. Various embodiments may providean efficient low complexity approach to compute the PES in the digitalservo-control loop that may be implemented in the system on chip (SoC)of a dual frequency dedicated servo system.

In various embodiments, position information, for example in the form ofposition error signal (PES), may be extracted from a readback servosignal and used as input to the servo controller for controlling thehead (e.g. read/write head) of a data storage device (e.g. a hard diskdrive (HDD)). In various embodiments, the position information or PESmay be extracted from the readback servo waveform by means of a PESdemodulator. The PES demodulator may be implemented as part of a servocontrol loop of the data storage device. Various embodiments may enablesimplification of the demodulator, thereby reducing the area requirementand power consumption of the SoC.

In various embodiments, the PES demodulator may employ a DiscreteFourier Transform (DFT) on the readback servo signal, where the PES maybe extracted or computed from the DFT. In one embodiment, the PESdemodulator may employ a sliding window Discrete Fourier Transform(DFT).

In general, a head-positioning servomechanism is provided in a datastorage device, e.g. a hard disk drive (HDD), which acts as a controlsystem. The control system may position the head (e.g. read/write (R/W)head) which is mounted on an actuator over a desired data track of astorage medium and reposition the head from one data track to another.

In a HDD servo control system, the position error signal (PES), andtherefore the position of the head relative to the center of the desireddata track, may be sensed and used by the servo system to generate theappropriate commands to the actuator, which in turn moves the head in aneffort to reduce the position error. PES is a signal proportional to therelative difference of the positions of the centre of the head and thenearest track centre. Therefore, PES may provide an indication of theposition of the head relative on the storage medium, for example theposition of the head relative to a data track, and whether the head ispositioned at the centre of the data track (on track) or shiftedrelative to the centre of the data track (off track) and the magnitudeof the shift, such that the position of the head may then be adjusted.

FIG. 1B shows a schematic block diagram of a servo control system 120,according to various embodiments. The system 120 receives a signal inthe form of data layer noise 122 (which is data layer signal but whichis considered as noise by the servo system), which is received by amultiplication circuit 124, which also receives an input, being aconstant scaling factor 1/SF, where SF<1, for multiplication of thesignals. The scaling factor is employed to account for the fact that thedata layer is closer to the reader and produces a stronger signal thanthe servo layer. The output, d_(n), models the data layer signal and isadded to s_(n), the servo signal 128, at summer (or summing circuit)126. The servo signal 128 models the servo layer signal. As the datalayer is closer to the reader of a head (e.g. read/write head) than theservo layer, it is multiplied by a scaling factor 1/SF.

The output, r_(n), of the summer 126 is provided to a filter 130 whichseparates the data signal d_(n) from the servo signal, s_(n). In oneembodiment, the filter 130 may be a bandpass filter (BPF). The outputfrom the filter 130 is then provided to a PES demodulator 132 to performextraction or demodulation in order to provide the position error signal(PES), PES_(n). Subsequently, a controller 134 receives the PES, andthen outputs a signal, u_(n), which together with another signal, d_(i),being the VCM input noise, are provided to a voice coil motor (VCM) 136.The VCM 136 may drive an actuator which controls the positioning of ahead (e.g. read/write head) in a data storage device. The output, y_(n),of the VCM 136 is fedback to the servo actuator which controls theposition of the head in the servo signal generating model 128. Theoutput y_(n) may include the VCM output noise, d_(o). d_(i) and d_(o)correspond to those illustrated in FIG. 1A. This block of the servocontrol system 120 may generate a simulated servo signal that may beused for testing the servo control loop. One difference between theservo control system 120 and the conventional servo control system 100(FIG. 1A) is that in the servo control system 120, processing is done ona sample-by-sample basis, and that the VCM position is updated eachsample. In the conventional servo control system 100, processing is doneon a block-by-block basis and the VCM position is updated over eachservo-control wedge. Sample-by-sample updating may be enabled by adedicated servo system and the continuous presence of servo information,as compared to the sporadic presence of servo information in an embeddedservo system. Another difference is with respect to the types of noisein the dedicated servo, where the noise at summer 104 (FIG. 1A)primarily consists of the noise d_(n) coming from the data layer summedat summer 126 (FIG. 1B).

In a dedicated servo implementation, one disk surface (servo layer) isdedicated to store the position data referred to as servo data or servosignal. The servo layer may be a buried layer arranged beneath the datarecording layer. Further, the servo layer and data recording layer maybe put or arranged on the same side or same plane, and they may be readand/or processed together; this may also be referred to as dedicatedservo. In various embodiments, there may be multiple (e.g. at least two)layers of magnetic media on a single surface, where one layer isdedicated to servo and another layer dedicated to data. The data layermay be arranged above the servo layer, thereby being closer to the headthan the servo layer. In contrast, conventionally, one surface of themagnetic media is dedicated to hold the servo, with no data being storedon this surface. In the context of various embodiments, the servo layerand the data recording layer are separate layers or distinct layerswhere the signals from the servo layer and the data layer may be readtogether at the same time. The signals from the servo layer and the datalayer may be read by a single head. The servo layer may have aperpendicular or a longitudinal magnetization orientation for providingmagnetic information for determining the location of the head inrelation to the storage medium. The servo information is provided on theservo layer distinct from the data recording layer so as to allowcontinuously available servo readback to enable continuous or continualposition feedback thereby providing continual location detection withoututilizing any of the recording layer for location detection. Thededicated servo may provide higher positioning accuracy throughcontinual location determination, while also removing the servosectors/tracks from the recording layer, thereby increasing surfaceutilization of the storage space in the recording layer and furtherincreasing the data recording density by increasing the trackpositioning accuracy.

The dedicated servo layer may have a continuous track structure having aplurality of servo tracks in a concentric arrangement. Adjacent servotracks may be alternately assigned different frequency signals, havingrespective frequencies f₁ and f₂, as illustrated in FIGS. 2A and 2B fora portion of the servo layer 200 towards its inner diameter, showingfour servo tracks 202 a, 202 b, 202 c, 202 d. In this configuration, thehead of the data storage device may be positioned in between twoadjacent tracks (e.g. 202 a and 202 b; 202 b and 202 c), for example atthe boundary of the two adjacent tracks, and may be able to obtain areadback servo signal having frequencies f₁ and f₂.

In further embodiments, adjacent servo tracks may be alternatelyassigned different frequency signals, for example three respectivefrequencies, four, five or any higher number, and the head may bepositioned in between any two adjacent tracks to obtain a readback servosignal having two different frequencies.

Therefore, in various embodiments of a dedicated servo system, eachservo track has a single frequency. The position error signal (PES) maybe extracted by means of DFT applied to, for example a dual frequencybased servo signal.

While not shown in FIGS. 2A and 2B, there may be small breaks in theservo tracks 202 a, 202 b, 202 c, 202 d for the sector address mark(SAM) and Gray code information, which contain addressing information.Providing this information may minimize any error that may lead towriting information on the wrong track, which may lead to a failure. Invarious embodiments, the SAM and/or Gray information may be written orprovided on both the data layer and the servo layer and such informationis not over-written. Therefore, the remaining portions of the servolayer contain servo information, e.g. frequency servo or ABCD burstpattern.

In order that the invention may be readily understood and put intopractical effect, particular embodiments will now be described by way ofexamples and not limitations, and with reference to the figures.

FIG. 3A shows a flow chart 300 illustrating a method for demodulating aposition error signal from a readback servo signal having a firstfrequency associated with a first servo track of a storage medium and asecond frequency associated with a second servo track adjacent to thefirst servo track, according to various embodiments.

At 302, the readback servo signal is sampled at successive time instantsto provide a sequence of samples. In other words, the readback servosignal may be sampled at a plurality of time instants so that thereadback servo signal may be represented by a plurality of discretevalues.

At 304, a Discrete Fourier Transform (DFT) is computed based on thesequence of samples.

At 306, a measurement indicative of the position error signal (PES) isprovided based on the Discrete Fourier Transform.

In various embodiments, a window of a predetermined length may beapplied to the sequence of samples to form a windowed sequence ofsamples and the Discrete Fourier Transform may be computed based on thewindowed sequence of samples. In various embodiments, the window has apredetermined length that is less than the length of the sequence ofsamples. In other words, the Discrete Fourier Transform is computedbased on a portion of the sequence of samples, where some samples maynot be utilised in the determination of the DFT.

In various embodiments, a sliding window of a predetermined length maybe applied to the sequence of samples to form respective windowedsequences of samples, wherein a respective Discrete Fourier Transformmay be computed based on each respective windowed sequence of samples,and subsequently a respective measurement indicative of the positionerror signal may be provided based on the respective Discrete FourierTransform.

In other words, a window of a predetermined length may be applied to thesequence of samples to form a windowed sequence of samples and theDiscrete Fourier Transform, from which the PES may be subsequentlydetermined, may be computed based on the windowed sequence of samples.The window may then be moved or shifted, for example by one timeinstant, and another DFT may be computed, from which another PES may bedetermined. This may be repeated as the sliding window is successivelymoved or cycled through the sequence of samples. Therefore, PES may bedetermined for different time instants based on the DFTs computed fordifferent time instants based on the respective positions of the slidingwindow.

In various embodiments based on the sliding window approach, for twoconsecutive windowed sequences of samples of the respective windowedsequences of samples, a respective Discrete Fourier Transform of asucceeding windowed sequence of samples of the two consecutive windowedsequences of samples may be computed based on a respective DiscreteFourier Transform computed based on a preceeding windowed sequence ofsamples of the two consecutive windowed sequences of samples. In otherwords, the DFT for the succeeding windowed sequence of samples need notnecessarily be computed based on the succeeding windowed sequence ofsamples of the two consecutive windowed sequences of samples, but ratherbased on or updated from the Discrete Fourier Transform computed basedon a preceeding windowed sequence of samples. Therefore, a new DFT, fora succeeding windowed sequence of samples, may be updated from theprevious DFT computation of a preceeding windowed sequence of samples.When the window slides over by one sample or one time instant, thesummation of the new (succeeding) DFT may substantially be written interms of the summation of the previous (preceeding) DFT. Thus, with acomplex multiplication and two complex additions, the new DFT sequencemay be obtained in terms of the old DFT sequence. This saves a lot ofcomputation, thereby providing computational efficiency.

In various embodiments, at 306, a difference between an absolute valueof a component of the Discrete Fourier Transform corresponding to thefirst frequency and an absolute value of a component of the DiscreteFourier Transform corresponding to the second frequency may be computedto provide the measurement indicative of the position error signal(PES). In other words, the modulus or absolute value of the component ofthe Discrete Fourier Transform of the readback servo signalcorresponding to the first frequency and the modulus or absolute valueof the component of the Discrete Fourier Transform of the readback servosignal corresponding to the second frequency may be determined and thedifference of these absolute values may be computed to provide the PES.

In the context of various embodiments, the component of the DiscreteFourier Transform may mean the coefficient of the Discrete FourierTransform.

FIG. 3B shows a schematic block diagram of a demodulator 320 fordemodulating a position error signal from a readback servo signal havinga first frequency associated with a first servo track of a storagemedium and a second frequency associated with a second servo trackadjacent to the first servo track, according to various embodiments. Thedemodulator 320 includes a sampling circuit 322 configured to sample thereadback servo signal at successive time instants to provide a sequenceof samples, and a computing circuit 324 configured to compute a DiscreteFourier Transform based on the sequence of samples, and furtherconfigured to provide a measurement indicative of the position errorsignal based on the Discrete Fourier Transform. In FIG. 3B, the linerepresented as 326 is illustrated to show the relationship between thesampling circuit 322 and the computing circuit 324, which may includeelectrical coupling and/or mechanical coupling, for example in terms ofthe arrangements of the sampling circuit 322 and the computing circuit324.

In the context of various embodiments, a “circuit” may be understood asany kind of a logic implementing entity, which may be special purposecircuitry or a processor executing software stored in a memory,firmware, or any combination thereof. Thus, in an embodiment, a“circuit” may be a hard-wired logic circuit or a programmable logiccircuit such as a programmable processor, e.g. a microprocessor (e.g. aComplex Instruction Set Computer (CISC) processor or a ReducedInstruction Set Computer (RISC) processor). A “circuit” may also be aprocessor executing software, e.g. any kind of computer program, e.g. acomputer program using a virtual machine code such as e.g. Java. Anyother kind of implementation of the respective functions which will bedescribed in more detail below may also be understood as a ‘circuit’ inaccordance with an alternative embodiment.

In the context of various embodiments, the demodulator 320 may include amemory which is for example used in the processing carried out by thedemodulator 320. A memory used in the embodiments may be a volatilememory, for example a DRAM (Dynamic Random Access Memory) or anon-volatile memory, for example a PROM (Programmable Read Only Memory),an EPROM (Erasable PROM), EEPROM (Electrically Erasable PROM), or aflash memory, e.g., a floating gate memory, a charge trapping memory, anMRAM (Magnetoresistive Random Access Memory) or a PCRAM (Phase ChangeRandom Access Memory).

In various embodiments, the computing circuit 324 may be configured toapply a window of a predetermined length to the sequence of samples toform a windowed sequence of samples, and further configured to computethe Discrete Fourier Transform based on the windowed sequence ofsamples.

In various embodiments, the computing circuit 324 may be configured toapply a sliding window of a predetermined length to the sequence ofsamples to form respective windowed sequences of samples, furtherconfigured to compute a respective Discrete Fourier Transform based oneach respective windowed sequence of samples, and further configured toprovide a respective measurement indicative of the position error signalbased on the respective Discrete Fourier Transform.

In various embodiments based on the sliding window approach, for twoconsecutive windowed sequences of samples of the respective windowedsequences of samples, the computing circuit 324 may be configured tocompute a respective Discrete Fourier Transform of a succeeding windowedsequence of samples of the two consecutive windowed sequences of samplesbased on a respective Discrete Fourier Transform computed based on apreceeding windowed sequence of samples of the two consecutive windowedsequences of samples.

In various embodiments, the computing circuit 324 may be configured tocompute a difference between an absolute value of a component of theDiscrete Fourier Transform corresponding to the first frequency and anabsolute value of a component of the Discrete Fourier Transformcorresponding to the second frequency.

In various embodiments, the demodulator 320 may form part of a datastorage device such as a hard disk drive (HDD). For example, thedemodulator 320 may be part of a servo control system in the HDD.

In the context of various embodiments, the measurement may be expressedas

PES_(m) =|X _(k) ^(m)|_(k=f1) −|X _(k) ^(m)|_(k=f2)  (Equation 1),

where

-   -   PES_(m) is the position error signal at time instant m,    -   |X_(k) ^(m)|_(k=f1) is the absolute value of the Discrete        Fourier Transform component of the readback servo signal        corresponding to frequency f₁, at time instant m,    -   |X_(k) ^(m)|_(k=f2) is the absolute value of the Discrete        Fourier Transform component of the readback servo signal        corresponding to frequency f₂, at time instant m,    -   f₁ is the first frequency,    -   f₂ is the second frequency.

In the context of various embodiments, m may be n; n+1; . . . ; n-w+1,where w is the window length.

In the context of various embodiments, the readback servo signal may bea continuous servo signal. In other words, the servo layer may provide acontinuous servo signal.

In the context of various embodiments, the readback servo signal isobtained or extracted from a dedicated servo layer of a storage medium,which is separate from the data recording layer of the storage medium.In one embodiment, the servo layer is arranged below the data recordinglayer, with the data recording layer being proximal to the head and theservo layer being distal to the head. The readback servo signal may beobtained by means of a head of the data storage device. The servo layerprovides servo information or positioning signals for servo control.

In the context of various embodiments, the servo layer may include aplurality of concentric tracks for holding the servo information. Eachservo track may be assigned or associated with a single frequencysignal. Adjacent servo tracks may be assigned different frequencies.Repeated servo tracks may be assigned alternate frequencies. In thecontext of various embodiments, adjacent servo tracks mean tracks thatare arranged side-by-side. In various embodiments, two adjacent servotracks share a common boundary. As illustrated by the non-limitingexamples of FIGS. 2A and 2B, two frequencies may be laid out side byside to define the servo tracks (and possibly, but not necessarily, thedata tracks too), with the head trying to fly down the center (boundary)of the two tracks, or off-center.

In the context of various embodiments, the term “head” may include amagnetic head. In addition, the “head” may refer to the read/write headfor reading/writing information or data from/to a storage medium. Thehead includes a reader and a writer. The head is positioned over astorage medium and the reader may read signal or information from thestorage medium and the writer may write information to the data layer ofthe storage medium.

In various embodiments, a sliding window Discrete Fourier Transform(DFT) may be computed or generated as discrete Fourier transform at thepoints sampled from a tap-delay line as illustrated in FIG. 4.

In various embodiments, a sequence of samples may be represented as

. . . ,x ⁻³ ,x ⁻² ,x ⁻¹ ,x ₀ ,x ₁ ,x ₂ ,x ₃ , . . . ,x _(n) ,x _(n+1), .. . .

By implementing a window or a sliding window of a predetermined length,w, for example at the time instant n, a windowed sequence of samplesincluding w samples, may be formed as

{x _(n-w+1) ,x _(n-w+2) ,x _(n-w+3) , . . . ,x _(n-2) ,x _(n+1) ,x_(n)},

A DFT sequence, X_(k), may then be performed on the windowed sequence ofsamples. At the time instant n, the DFT may be computed as follows

$\begin{matrix}{X_{k}^{n} = {\sum\limits_{i = 0}^{w - 1}{x_{n - i}{^{- \frac{j\; 2\; \pi \; \; k}{w}}.}}}} & ( {{Equation}\mspace{14mu} 2} )\end{matrix}$

In addition, at the succeeding time instant n+1, the DFT may be computedas follows

$\begin{matrix}{X_{k}^{n + 1} = {\sum\limits_{i = 0}^{w - 1}{x_{n + 1 - i}{^{- \frac{j\; 2\; \pi \; \; k}{w}}.}}}} & ( {{Equation}\mspace{14mu} 3} )\end{matrix}$

A sliding window Discrete Fourier Transform (DFT) approach may providecomputational efficiency as the windowed sequences for two successivetime instances, e.g. at n−1 and n; and at n and n+1, contain essentiallyidentical elements.

For a DFT of size w, if the w-DFT of x_(n) is X_(k), then

$\begin{matrix} x_{n - p}rightarrow{X_{k}{^{\frac{{- j}\; 2\; \pi \; {kp}}{w}}.}}  & ( {{Equation}\mspace{14mu} 4} )\end{matrix}$

Equation 4 shows the DFT of a circularly shifted sequence. If a sequenceis circularly shifted by one sample (to the left), then the DFT valueX_(k) becomes

$\begin{matrix} X_{k}arrow{X_{k}{^{\frac{j\; 2\; \pi \; k}{w}}.}}  & ( {{Equation}\mspace{14mu} 5} )\end{matrix}$

Hence, the DFTs of two successive windowed sequences, X_(k) ^(n+1) andX_(k) ^(n), each of length w, x_(n+1) and x_(n-w+1) may be related as:

$\begin{matrix}{{X_{k}^{n + 1} = {{^{- \frac{j\; 2\; \pi \; k}{w}}X_{k}^{n}} + ( {x_{n + 1} - x_{n - w + 1}} )}},} & ( {{Equation}\mspace{14mu} 6} )\end{matrix}$

Therefore, Equation 6 may be used for updating the sliding window DFT.

Equation 6 allows updating of the DFT sequence X_(k) at time (n+1) interms of X_(k) at time (n). Equation 6 shows that the update equationrequires only one complex multiplication and two additions to beimplemented per DFT point, which is less complex than O(w log w) neededusing the most efficient FFT (Fast Fourier Transform) algorithms, wherew is the window length of the DFT and “O” is the big O notation asgenerally used in Mathematics to describe the limiting behavior of afunction when the argument/input of the function tends towards aparticular value or infinity.

Based on Equation 6, the DFT sequence at a particular time instant (e.g.X_(k) ^(n+1)) may be updated or computed based on the DFT sequence ofthe immediately preceeding time instant (e.g. X_(k) ^(n)), the sample atthe particular time instant whose DFT sequence is to be computed (e.g.x_(n+1)), and the sample at the final time instant within the window oflength w (e.g. x_(n-w+1)).

The PES demodulator output may then be computed as the differencebetween the absolute value of the respective X_(k) or the DFT componentsof the readback servo signal at the two frequencies of a dual frequencybased servo signal employed in the data storage device. The PES may becomputed based on the following equation,

PES_(m) =|X _(k) ^(m)|_(k=f1) −|X _(k) ^(m)|_(k=f2)  (Equation 7),

where

-   -   PES_(m) is the position error signal at time instant m,    -   |X_(k) ^(m)|_(k=f1) is the absolute value of the Discrete        Fourier Transform component of the readback servo signal        corresponding to frequency f₁, at time instant m,    -   |X_(k) ^(m)|_(k=f2) is the absolute value of the Discrete        Fourier Transform component of the readback servo signal        corresponding to frequency f₂, at time instant m,    -   f₁ and f₂ refer to the respective frequencies of a dual        frequency based servo signal employed in a data storage device.

In various embodiments, m may be n; n+1; . . . ; n-w+1, where w is thewindow length.

In further embodiments, the PES may be computed based on the followingequation,

PES_(m) =A×(|X _(k) ^(m)|_(k=f1) −|X _(k) ^(m)|_(k=f2))  (Equation 8),

where

-   -   PES_(m) is the position error signal at time instant m,    -   |X_(k) ^(m)|_(k=f1) is the absolute value of the Discrete        Fourier Transform component of the readback servo signal        corresponding to frequency f₁, at time instant m,    -   |X_(k) ^(m)|_(k=f2) is the absolute value of the Discrete        Fourier Transform component of the readback servo signal        corresponding to frequency f₂, at time instant m,    -   f₁ and f₂ refer to the respective frequencies of a dual        frequency based servo signal employed in a data storage device,    -   A is a normalization factor.

In various embodiments, m may be n; n+1; . . . ; n-w+1, where w is thewindow length.

In various embodiments, as the head may be off-set in the verticaldirection relative to the storage medium, due for example to fly-heightvariation, the readback servo signal may correspondingly decrease whenthe head is further from the servo layer and the storage medium, andnormalization of the servo signal may be required as otherwise theoutput of the servo controller may be too weak to compensate for thecross-track offset. This may then provide an improved or accuratemeasure of the head's cross-track position that may then be effectivelyused for servo control.

Using ABCD servo-burst-signal pattern as a non-limiting example, PES maybe computed as (A−B)/(A+B) where A and B denote the amplitudes of twosignals containing cross-track information. For example, with ABCD (orjust AB) servo, A and B may be the respective amplitudes of two servofrequency bursts appropriately offset in the cross-track direction. Whenthe head happens to be too much towards the A burst, then the A signalis stronger, and the B burst is weaker and a positive PES=(A−B)/(A+B)may be obtained, indicating the proximity of the head towards the Aburst. When the head is too much towards the B burst, the inverse holdsand a negative PES may be obtained, indicating the proximity of the headtowards the B burst. The controller may be interested in the relativestrength of (A−B), which for example may be normalized, e.g. using(A+B).

Normalization of (A−B) may be required as illustrated by the followingnon-limiting example. The head may be off-set in the vertical direction,due to fly-height variation. Both A and B signals may correspondinglydecrease because the head may be further from the storage medium. Where(A−B) is not normalized appropriately, the output of the servocontroller may be too weak to compensate for the cross-track offset.Where the head is offset vertically due to fly-height variation, then(A+B) may also correspondingly decrease in amplitude such that(A−B)/(A+B) may still give an accurate measure of the head's cross-trackposition that may then be effectively used for servo control.

As a non-limiting example, f₁ may be 30 MHz, and f₂ may be 40 MHz. Inaddition, as a non-limiting example, A may be |X_(k) ^(m)|_(k=f1)+|X_(k)^(m)|_(k=f2).

In various embodiments, applying a window, including a sliding window,on the sequence of samples, from which a DFT is computed may provide asimplified approach as PES may be determined from the respectivecomponents of the Discrete Fourier Transform corresponding to thefrequencies associated with the servo signal. In addition, the slidingwindow approach may allow the DFT at a particular time instant to beupdated based on the DFT of the preceeding time instant. Accordingly,the respective components of the DFT of the readback servo signalcorresponding to the respective frequencies associated with the servosignal may be updated based on the respective components of the DFT at apreceeding time instant. In this approach, components of the DiscreteFourier Transform corresponding to any other frequencies may not berequired to determine PES and therefore uneeded information need not betaken into consideration or computed. In contrast, by using a FastFourier Transform (FFT), each computation of the FFT sequence requirescomputation of FFT corresponding to all the samples, where all but twoof which are subsequently not utilised.

FIG. 5 shows a plot 500 of comparison of results of the sliding windowDiscrete Fourier Transform (DFT) 502 and a direct computational approach504 for extracting PES. As examples, the direct computational approachmay be a double summation of the DFT or the FFT algorithm. The plot 500was obtained from a simulation that computes the DFT of the readbackservo signal having the data signal with the two servo frequencies. Thevertical y-axis is the DFT of the readback servo signal (absolutevalue), and the horizontal x-axis is the normalized frequency. The DFTwas computed through 2 methods: the direct method (which is slower) andthe sliding window method (which is faster). The results shows that thesliding window DFT computation produces exactly the same result as theslower direct computation. As shown in FIG. 5, the results for thesliding window DFT 502 and the direct computation 504 overlap eachother, in other words, the results lie on top of each other, therebyillustrating substantially perfect correlation of both sets of results.

The DFT changes with time as the head moves between the two servo trackspicking up different quantities of the two sinusoidal signals of theservo signal having respective frequencies. The plot 500 is a snap-shotof the time-evolution of the DFT at a particular time instant. At thistime instant, the PES is given as the difference of the amplitude of thetwo frequencies PES=(A1−A2)/(A1+A2), where A1 and A2 are the amplitudesof the two frequencies, estimated from the sliding window DFT. These twofrequencies are visible in the spectrum as the two spikes at aroundfrequencies 0.04 and 0.05, which are marked with “O” and pointed at witharrows in FIG. 5.

Therefore, using a sliding window DFT approach may replace the directDFT or direct computation approach, allowing the PES to be demodulatedfrom the readback servo signal.

FIGS. 6A to 6D show plots of results corresponding to a demodulatedposition error signal (PES) with no servo control or with servo control,and with no data layer noise or with data layer noise, according tovarious embodiments. FIGS. 6A to 6D show the results for ref 602, PES604, force 606, offset 608, A1 610 and A2 612. The servo control system120 of the embodiment of FIG. 1B was used to model the signals andgenerate the performance plots of FIGS. 6A to 6D.

FIGS. 6A, 6B, 6C and 6D show non-limiting examples of the varioussignals in a continuous servo modulating system in four separatescenarios: with and without data-layer noise, and with servo control onand servo control off. In the case of these non-limiting examples, noiseas injected at summer 126 (FIG. 1B) includes the unwanted signal fromthe data layer. In the case of these examples, a simple non-limitingexample of a servo control algorithm may be implemented to demonstratethe principles described. “Servo control on” refers to the utilizationof y_(n) information within the servo signal block 128 to generate thereadback signal (FIG. 1B), while servo control off refers to thenon-utiliazation of y_(n) information within the servo signal block 128to generate the readback signal (FIG. 1B).

Signal 602 refers to the reference signal ref_(n) in FIG. 1B and in theexamples of FIGS. 6A, 6B, 6C and 6D, is a linear disturbance downwardsuntil time-index 15000 followed by a sharper linear disturbance upwardsuntil time-index 30000. Within the servo signal block 128 (FIG. 1B),there exists a time-domain summation of 2 sinusoids weighted inamplitude by the difference between the reference signal ref_(n) and thecontrol signal y_(n). These amplitudes are depicted by the signals A1610 and A2 612 in FIGS. 6A, 6B, 6C and 6D, and are determined by thedifference between the ref_(n) signal 602 and the head offset signal608. Within the context of this simulation, the head-offset signal 608is either zero, when servo control is off, or it is the damped responseof the applied force, when servo control is turned on. Within thenon-limiting context of this simulation, the force 606 applied at theVCM coil is turned on fully when the PES signal 604 exceeds a threshold,otherwise the force 606 applied is turned off. The PES signal 604 inthis simulation is generated as the difference in amplitude of the twosinusoidal frequencies as estimated by the sliding window DFT asdescribed above.

Given the above definitions, the working of the sliding window DFT in asimple servo-control simulation may be demonstrated. FIG. 6A shows thecase with open servo loop (no control) and with no data noise injectedfor the computation of the PES. The open-loop means that the appliedforce 606 does not impact the head offset, hence the signal 608 isalways zero, and the amplitudes A1 610 and A2 612 of the two sinusoidssimply follow the reference signal 602. The PES signal 604 is computedfrom the amplitudes A1 610 and A2 612 using the sliding window DFT andis found to follow the reference signal 602 closely. The force signal606 turns on, and pushes the head back towards the track center based onthe PES signal 604, but in the case of FIG. 6A which is open-loop, thisforce 606 is unconnected to the head offset 608 and therefore has nobearing on the head-position.

FIG. 6B shows what happens when the data signal, which is considerednoise, is included. The PES signal 604 becomes noisier due to thepresence of the data signal, and thus the force 606 applied at the VCMalso becomes noisier. However the VCM force 606 is still uncoupled tothe head offset 608 and thus sinusoidal amplitudes A1 610 and A2 612follow the reference signal 602 as before. The PES 604 also follows thereference signal 602, but with noise showing that the computed PES is anoisy measure of the off-track position of the head.

FIG. 6C shows the results when the servo loop is closed, in the casewithout data-layer noise. Under these conditions, the applied force 606has an impact on the head offset position 608 and the head moves untilit counteracts the disturbance in the reference signal 602. The headfollowing the disturbance in an on-off manner keeps the amplitudes ofthe two servo sinusoids A1 610 and A2 612, both close to one half, i.e.near the track center. When the reference signal 602 turns around attime-instant 15000, the relative amplitudes of the two servo sinusoidsA1 610 and A2 612 reverses and pushes the head back in the oppositedirection. The larger gradient of the reference signal 602 results inthe force 606 being turned on for a longer time in order to keep thehead close to the reference signal 602.

FIG. 6D shows the results having both servo control on and data-layernoise on. It may be observed that the head is still able to track thereference signal 602 albeit in a more noisy manner.

These simulations demonstrate the feasibility of the approach of variousembodiments using the sliding window DFT, e.g. including a windowed DFTor a sliding windowed DFT, and updating the signals every iterationinstead of once per block. In the context of various embodiments, areference to updating the signals may refer to updating of the servocontinuously, which may be enabled by the presence of continuous servoinformation, for example as all-the-time servo (ATTS) as shown in thebottom half of FIG. 7. In the ATTS embodiment, the servo is not turnedoff, except possibly over the SAM and Gray information. Therefore, thereis controlling (servo control) all the time, hence the term“all-the-time servo”.

The approach of various embodiments may be employed to extract PES fromthe servo signal of a servo layer having any servo pattern, for exampleany continual or continuous servo pattern, and/or servo pattern havingany number of servo tracks (i.e. any density or bandwidth), includingall-the-time servo in which servo information is provided throughout theentire servo layer where the servo information is available all thetime, thereby providing a dedicated servo system., as illustrated inFIG. 7. In the 2× servo bandwidth embodiment, the presence of continuousservo information may be used to control the head more frequently, akinto having more “spokes” (dark coloured) around the circumference, asshown in FIG. 7. There are still regions (smaller regions) in which theservo information is not actuating the head, and just fly blind, similarto embedded servo, between the spokes.

The approach of various embodiments may simplify the servo computationsfor the system on chip (SoC), for example including using all-the-timeservo (ATTS). For example, as demonstrated by the above simulationresult and the complexity of the servo demodulation scheme, only acomplex multiply and two complex additions are required per sample.

While the invention has been particularly shown and described withreference to specific embodiments, it should be understood by thoseskilled in the art that various changes in form and detail may be madetherein without departing from the spirit and scope of the invention asdefined by the appended claims. The scope of the invention is thusindicated by the appended claims and all changes which come within themeaning and range of equivalency of the claims are therefore intended tobe embraced.

1. A method for demodulating a position error signal from a readbackservo signal having a first frequency associated with a first servotrack of a storage medium and a second frequency associated with asecond servo track adjacent to the first servo track, the methodcomprising: sampling the readback servo signal at successive timeinstants to provide a sequence of samples; computing a Discrete FourierTransform based on the sequence of samples; and providing a measurementindicative of the position error signal based on the Discrete FourierTransform.
 2. The method as claimed in claim 1, further comprising:applying a window of a predetermined length to the sequence of samplesto form a windowed sequence of samples; wherein computing the DiscreteFourier Transform comprises computing the Discrete Fourier Transformbased on the windowed sequence of samples.
 3. The method as claimed inclaim 1, further comprising: applying a sliding window of apredetermined length to the sequence of samples to form respectivewindowed sequences of samples; wherein computing the Discrete FourierTransform comprises computing a respective Discrete Fourier Transformbased on each respective windowed sequence of samples, and whereinproviding the measurement comprises providing a respective measurementindicative of the position error signal based on the respective DiscreteFourier Transform.
 4. The method as claimed in claim 3, wherein for twoconsecutive windowed sequences of samples of the respective windowedsequences of samples, computing the Discrete Fourier Transform comprisescomputing a respective Discrete Fourier Transform of a succeedingwindowed sequence of samples of the two consecutive windowed sequencesof samples based on a respective Discrete Fourier Transform computedbased on a preceeding windowed sequence of samples of the twoconsecutive windowed sequences of samples.
 5. The method according toclaim 1, wherein providing the measurement comprises computing adifference between an absolute value of a component of the DiscreteFourier Transform corresponding to the first frequency and an absolutevalue of a component of the Discrete Fourier Transform corresponding tothe second frequency.
 6. The method according to claim 1, wherein themeasurement is expressed as:PES_(m) =|X _(k) ^(m)|_(k=f1) −|X _(k) ^(m)|_(k=f2) where PES_(m) is theposition error signal at time instant m, |X_(k) ^(m)|_(k=f1) representsthe absolute value of the Discrete Fourier Transform component of thereadback servo signal corresponding to frequency f₁, at time instant m,|X_(k) ^(m)|_(k=f2) represents the absolute value of the DiscreteFourier Transform component of the readback servo signal correspondingto frequency f₂, at time instant m, f₁ is the first frequency, f₂ is thesecond frequency.
 7. A demodulator for demodulating a position errorsignal from a readback servo signal having a first frequency associatedwith a first servo track of a storage medium and a second frequencyassociated with a second servo track adjacent to the first servo track,the demodulator comprising: a sampling circuit configured to sample thereadback servo signal at successive time instants to provide a sequenceof samples; a computing circuit configured to compute a Discrete FourierTransform based on the sequence of samples, and further configured toprovide a measurement indicative of the position error signal based onthe Discrete Fourier Transform.
 8. The demodulator as claimed in claim7, wherein the computing circuit is configured to apply a window of apredetermined length to the sequence of samples to form a windowedsequence of samples, and further configured to compute the DiscreteFourier Transform based on the windowed sequence of samples.
 9. Thedemodulator as claimed in claim 7, wherein the computing circuit isconfigured to apply a sliding window of a predetermined length to thesequence of samples to form respective windowed sequences of samples,further configured to compute a respective Discrete Fourier Transformbased on each respective windowed sequence of samples, and furtherconfigured to provide a respective measurement indicative of theposition error signal based on the respective Discrete FourierTransform.
 10. The demodulator as claimed in claim 9, wherein for twoconsecutive windowed sequences of samples of the respective windowedsequences of samples, the computing circuit is configured to compute arespective Discrete Fourier Transform of a succeeding windowed sequenceof samples of the two consecutive windowed sequences of samples based ona respective Discrete Fourier Transform computed based on a preceedingwindowed sequence of samples of the two consecutive windowed sequencesof samples.
 11. The demodulator as claimed in claim 7, wherein thecomputing circuit is configured to compute a difference between anabsolute value of a component of the Discrete Fourier Transformcorresponding to the first frequency and an absolute value of acomponent of the Discrete Fourier Transform corresponding to the secondfrequency.
 12. The demodulator according to claim 7, wherein themeasurement is expressed as:PES_(m) =|X _(k) ^(m)|_(k=f1) −|X _(k) ^(m)|_(k=f2) where PES_(m) is theposition error signal at time instant m, |X_(k) ^(m)|_(k=f1) representsthe absolute value of the Discrete Fourier Transform component of thereadback servo signal corresponding to frequency f₁, at time instant m,|X_(k) ^(m)|_(k=f2) represents the absolute value of the DiscreteFourier Transform component of the readback servo signal correspondingto frequency f₂, at time instant m, f₁ is the first frequency, f₂ is thesecond frequency.